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Q.

When two resistors with resistance $5 Ω$ and $10 Ω$ are connected to $6 V$ emf battery, then the minimum current drawn from the circuit is

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a

0.4 A

b

2 A

c

5 A

d

None of the above

answer is A.

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Detailed Solution

When two resistors with resistance

5 Ω

and

10 Ω

are connected to

6 V

emf battery, then the minimum current drawn from the circuit is

0.4 A

.
It is given that two resistors of resistances

5 Ω

and

10 Ω

are connected to

6 V

emf battery.
According to the Ohm’s law, “the potential difference

(V)

across two terminals is directly proportional to the flow of current

(I)

across the circuit.” Mathematically,

V = IR

or

\Rightarrow I = \frac{V}{R}

Where

R

is the resistance.
Hence, it can be observed that the current and resistance is inversely proportional to each other. It is known that when the resistors are connected in series then the value of resistance is maximum which in turn allows minimum current to flow through the circuit. The equivalent resistance is given by

R_{S} = 5 + 10

\Rightarrow R_{S} = 15 Ω

Let

I_{\min}

represent the minimum current flowing through the circuit. Now, from Ohm’s law, the minimum current in the circuit is equal to

I_{\min} = \frac{V}{R_{S}}

On substituting the given values, we get the minimum current

I_{\min}

as

\Rightarrow I_{\min} = \frac{6}{15}

\Rightarrow I_{\min} = 0.4 A

Hence, the minimum current through the circuit is

0.4 A

.

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